Staff Profile

Roles and Responsibilities

• Chair of the PEC committee, School of MSP, 2021-2022.
• Research Group Leader, Pure Group, 2012 - 2019.
• Member of the Editorial Advisory Board of the International Open Access Electronic Journal ``Topological Algebras and their Applications" 2012 - 2024 http://www.degruyter.com/view/j/taa/ .
• Member of the Editorial Board of the International Open Access Electronic Journal ``Annals of Functional Analysis", 2010 - present  https://www.springer.com/journal/43034/ .
• Member of the Steering Committee of the International Conference on Banach Algebras and their Applications, 2005 - present.
• EPSRC Full College member.

Qualifications

• BSc, MSc, D.Phil., Moscow State University;
• Dotsent, the State Committee of the Russian Federation for Higher Education

Areas of expertise

•  Mathematical Analysis
•   Complex Analysis
•  Operators on Hilbert spaces
•   Interpolation problems
•  Homological theory of topological algebras
•  Extensions of topological algebras
•  Cyclic type (co)homology of topological algebras
•  Higher-dimensional amenability of Banach algebras
•  C*-algebras

ORCID: Click here.

Google Scholar: Click here

Research Interests

 Mathematical Analysis

 Operators on Hilbert space

 Complex analysis

 Interpolation problems

 Homological theory of topological algebras

 Extensions of topological algebras

 Cyclic type (co)homology of topological algebras

 Higher-dimensional amenability of Banach algebras

 C*-algebras

PhD projects

http://www.mas.ncl.ac.uk/~nzal/PhD_Projects.pdf

Research PhD students:

• Mr Connor Evans

Theses of former PhD students:

 David Cushing (PhD 2015)   http://theses.ncl.ac.uk/jspui/handle/10443/3024/ 

 David Brown (PhD 2016)  https://theses.ncl.ac.uk/jspui/handle/10443/3532/

 Amos Ajibo (PhD 2019) https://theses.ncl.ac.uk/jspui/handle/10443/4507

 Omar Alsalhi (PhD 2019) http://theses.ncl.ac.uk/jspui/handle/10443/4836 

 Hadi Alshammari (PhD 2019) http://theses.ncl.ac.uk/jspui/handle/10443/4819

 Dimitrios Chiotis (PhD 2020)  http://theses.ncl.ac.uk/jspui/handle/10443/4911 

Nujood Mued J Alshehri (PhD 2023) http://theses.ncl.ac.uk/jspui/handle/10443/6205

Undergraduate Teaching

2024-2025

MAS2702 Complex Analysis

https://www.ncl.ac.uk/module-catalogue/module.php?code=MAS2702

MAS3091 Group Project

https://www.ncl.ac.uk/module-catalogue/module.php?code=MAS3091

MAS8756 Functional Analysis

https://www.ncl.ac.uk/module-catalogue/module.php?code=MAS8756

PhD projects

http://www.mas.ncl.ac.uk/~nzal/PhD_Projects.pdf

• Articles

  • Agler J, Lykova ZA, Young NJ. Function theory in the bfd-norm on an elliptical region. Journal of Mathematical Analysis and Applications 2025, 541(2), 128732.
  • Agler J, Lykova ZA, Young NJ. On the operators with numerical range in an ellipse. Journal of Functional Analysis 2024, 287(8), 110556.
  • Alshehri NM, Lykova ZA. A Schwarz lemma for the pentablock. The Journal of Geometric Analysis 2023, 33, 65.
  • Agler J, Lykova ZA, Young NJ. A Hilbert space approach to singularities of functions. Journal of Functional Analysis 2023, 284(6), 109826.
  • Alsalhi OMO, Lykova ZA. Rational tetra-inner functions and the special variety of the tetrablock. Journal of Mathematical Analysis and Applications 2022, 506(1), 125534.
  • Agler J, Lykova ZA, Young NJ. Nonuniqueness of Carathéodory extremal functions on the symmetrized bidisc. Analysis Mathematica 2022, 48, 287-306.
  • Agler J, Lykova ZA, Young NJ. Intrinsic Directions, Orthogonality and Distinguished Geodesics in the Symmetrized Bidisc. The Journal of Geometric Analysis 2021, 31, 8202-8237.
  • Alshammari HO, Lykova ZA. Interpolation by holomorphic maps from the disc to the tetrablock. The Journal of Mathematical Analysis and Applications 2021, 498(2), 124951.
  • Chiotis D, Lykova ZA, Young NJ. Exterior products of operators and superoptimal analytic approximation. Transactions of the London Mathematical Society 2021, 8(1), 299-412.
  • Chiotis D, Lykova ZA, Young NJ. Exterior powers and pointwise creation operators. Complex Analysis and Operator Theory 2021, 15, 29.
  • Agler J, Lykova Z, Young N. Geodesics, retracts, and the norm-preserving extension property in the symmetrized bidisc. Memoirs of the American Mathematical Society 2019, 258(1242), 1-108.
  • Agler J, Lykova ZA, Young NJ. Characterizations of some domains via Carathéodory extremals. Journal of Geometric Analysis 2019, 29(4), 3039–3054.
  • Agler J, Lykova ZA, Young NJ. A geometric characterization of the symmetrized bidisc. Journal of Mathematical Analysis and Applications 2019, 473(2), 1377-1413.
  • Agler J, Lykova ZA, Young NJ. Algebraic and geometric aspects of rational Γ-inner functions. Advances in Mathematics 2018, 328, 133-159.
  • Agler J, Lykova ZA, Young NJ. Finite Blaschke products and the construction of rational $\Gamma$-inner functions. Journal of Mathematical Analysis and Applications 2017, 447(2), 1163–1196.
  • Brown DC, Lykova ZA, Young NJ. A rich structure related to the construction of analytic matrix functions. Journal of Functional Analysis 2017, 272(4), 1704-1754.
  • Agler J, Lykova Z, Young NJ. The complex geometry of a domain related to μ-synthesis. Journal of Mathematical Analysis and Applications 2015, 422(1), 508-543.
  • Agler J, Lykova ZA, Young NJ. 3-extremal holomorphic maps and the symmetrised bidisc. Journal of Geometric Analysis 2015, 25(3), 2060-2102.
  • Cushing D, Lykova ZA. Projectivity of Banach and C*-algebras of continuous fields. Quarterly Journal of Mathematics 2013, 64(2), 341-371.
  • Agler J, Lykova ZA, Young NJ. Extremal holomorphic maps and the symmetrized bidisc. Proceedings of the London Mathematical Society 2013, 106(4), 781-818.
  • Agler J, Lykova ZA, Young NJ. A Case of $\mu$-Synthesis as a Quadratic Semidefinite Program. SIAM Journal on Control and Optimization 2013, 51(3), 2472-2508.
  • Lykova ZA. The higher-dimensional amenability of tensor products of Banach algebras. Journal of Operator Theory 2012, 67(1), 73-100.
  • Agler J, Lykova ZA, Young NJ. Pseudo-Taylor expansions and the Carathéodory-Fejér problem. Journal of Mathematical Analysis and Applications 2012, 386(1), 308-318.
  • Agler J, Lykova ZA, Young NJ. The boundary Carathéodory–Fejér interpolation problem. Journal of Mathematical Analysis and Applications 2011, 382(2), 645-662.
  • Lykova ZA. Hochschild cohomology of tensor products of topological algebras. Proceedings of the Edinburgh Mathematical Society 2010, 53, 447-470.
  • Lykova ZA. Cyclic cohomology of certain nuclear Fréchet and DF algebras. Central European Journal of Mathematics 2008, 6(3), 405-421.
  • Lykova ZA. Cyclic-type cohomology of strict inductive limits of Fréchet algebras. Journal of Pure and Applied Algebra 2006, 205(3), 471-497.
  • Lykova ZA. Cyclic cohomology of projective limits of topological algebras. Proceedings of the Edinburgh Mathematical Society 2006, 49(1), 173-199.
  • Gourdeau F, Lykova ZA, White MC. A Künneth formula in topological homology and its applications to the simplicial cohomology of ℓ¹(ℤ+^k). Studia Mathematica 2005, 166(1), 29-54.
  • Lykova ZA. Relations between the homologies of C*-algebras and their commutative C*-subalgebras. Mathematical Proceedings of the Cambridge Philosophical Society 2002, 132, 155-168.
  • Brodzki J, Lykova ZA. Excision in cyclic type homology of Fréchet algebras. Bulletin of the London Mathematical Society 2001, 33(3), 283-291.
  • Lykova ZA. Relative cohomology of Banach algebras. Journal of Operator Theory 1999, 41(1), 23-53.
  • Bade WG, Dales HG, Lykova ZA. Algebraic and strong splittings of extensions of Banach algebras. Memoirs of the American Mathematical Society 1999, 137(656), 1-113.
  • Lykova ZA. Excision In Banach Simplicial And Cyclic Cohomology. Proceedings of the Edinburgh Mathematical Society 1998, 41(2), 411-427.
  • Lykova ZA. Examples of Banach algebras over commutative Banach algebras with given homological dimension. Communications in Algebra 1998, 26(6), 1779-1793.
  • Lykova ZA. A lower estimate of the global homological dimension of infinite-dimensional CCR-algebras. In 'Operator algebras and topology'. Proceedings of the OATE 2 Conference: Romania. Pitman Research Notes in Mathematics, no. 270, Longman Scientific and Technical, England, 1992, 93-129 1989.

• Book Chapters

  • Lykova ZA, Young NJ, Ajibo AE. Analytic interpolation into the tetrablock and a μ-synthesis problem. In: Bolotnikov V; ter Horst S; Ran ACM; Vinnikov V, ed. Interpolation and Realization Theory with Applications to Control Theory. Basel: Springer, 2019, pp.235-247.
  • Agler J, Lykova ZA, Young NJ. Carathéodory extremal functions on the symmetrized bidisc. In: Bart, H; ter Horst, S; Ran, ACM; Woerdeman, HJ, ed. Operator Theory, Analysis and the State Space Approach. Birkhäuser Basel: Birkhaeuser Science, 2018, pp.1-21.
  • Lykova ZA, Gourdeau F, White MC. The simplicial cohomology of L1(Rk+). In: To-Ming Lau, A., Runde, V, ed. Branch Algebras and Their Applications. Providence, Rhode Island, USA: American Mathematical Society, 2005, pp.95-109.